few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Calculate expected values and use them to solve problems.

Draw informal comparative inferences about two populations.

Understand and evaluate random processes underlying statistical experiments.

Investigate chance processes and develop, use, and evaluate probability models.

Summarize, represent, and interpret data on a single count or measurement variable.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Interpret linear models.

Summarize and describe distributions.

Understand independence and conditional probability and use them to interpret data.

Use random sampling to draw inferences about a population.

Develop understanding of statistical variability.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Use probability to evaluate outcomes of decisions.

Investigate patterns of association in bivariate data.
problem_activity: Task
Bob’s Bagel Shop has estimated the following probabilities for the number of bagels a randomly-selected customer buys when he or she enters the shop.
| No. of Bagels | Probability |
|---------------|-------------|
|       1       |     .5      |
|       2       |     .1      |
|       3       |     .1      |
|       6       |     .1      |
|      12       |     .2      |
Bob sells bagels for \$0.80 each, or \$9.00 for a dozen. If $X =$ the amount of money Bob collects from a randomly-selected customer, find and interpret the expected value of $X$.


correct_option_index: 0